Continuous deformations of harmonic maps and their unitons

Alexandru Aleman, María J. Martín*, Anna Maria Persson, Martin Svensson

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.

Original languageEnglish
JournalMonatshefte fur Mathematik
Issue number4
Pages (from-to)599-614
Number of pages16
Publication statusPublished - 1. Dec 2019


  • Blaschke–Potapov products
  • Bruhat decomposition
  • Extended solutions
  • Harmonic maps
  • Shift-invariant subspaces
  • Unitons


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